Abel means for orthogonal expansions of distributions on spheres, balls and simplices

A point is out of the support of a distribution on the open standard simplex if and only if the orthogonal expansion of the distribution is uniformly summable in Abel means to zero on a neighborhood of the point. A similar equivalence holds for Fourier-Laplace series on the unit sphere and orthogonal expansions on the open unit ball. (C) 2015 Elsevier Inc. All rights reserved.